Stochastic invertibility on Wiener space: some general results, and applications
2012-10-12 14:30 2012-10-12 15:30 2012-10-12 14:30 .. 15:30
Rémi Lassalle (Télécom Paristech)
I will begin with an introduction to invertibility of adapted shifts on Wiener space. In particular I will recall the main results which play a key role in the applications. Then I will investigate many applications to various fields i.e. to information theory, stochastic mechanics, and optimal transport. In particular I will give a general result of pathwise uniqueness for the stochastic picture of quantum euclidean mechanics, and I will extend Shannon's inequality to any abstract Wiener space. I will also show that the proof of this inequality relies on information loss in Gaussian channels. Finally, I will explain how our results can fit in more geometrical frameworks, such as the space of the paths with values in a finite dimensional Lie group.